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The MCTM Elementary Math Contest: Who Participates and Who Wins

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Title: The MCTM Elementary Math Contest: Who Participates and Who Wins


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2
The MCTM Elementary Math Contest Who
Participates and Who Wins?
  • Dr. David Ashley, dia059_at_smsu.edu
    math.smsu.edu/faculty/ashley.html
  • Dr. Lynda Plymate, lsm953f_at_smsu.edu
  • math.smsu.edu/lynda

Department of Mathematics Southwest Missouri
State University Springfield, MO 65804
3
Test Background
  • MCTM Annual Exam
  • 25 Regional Sites
  • Grades 4,5, and 6
  • Schools Select Participants 3-5/Grade Level
  • Concepts Exam (24)Problem Solving (18)
  • Exams measure conceptual understanding and
    problem solving ability.
  • The top three winners go to State.

4
Research Design/Methodology
  • Regional survey (10 Items)
  • Parent Survey (30 Items)
  • Exam Analysis
  • Concept/Problem Solving
  • Conceptual/ Procedural
  • NCTM Content Standards

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Who Participated in 2004?
  • 2783 Contestants at 25 Sites
  • 4th Grade 956 students
  • 5th Grade 939 students
  • 6th Grade 888 students
  • 388 State Finalists
  • 4th Grade 127 students
  • 5th Grade 132 students
  • 6th Grade 129 students

7
Regional Test Results
8
State Finals Test Results
9
Regional Data Survey Results
10
Regional Data Survey Results
11
Regional Data Survey Results
12
Informal Findings
  • From our parent survey, we found that there were
    no significant differences on how males and
    females were selected for the contest (57 took
    preliminary tests) or prepared for the contest
    (75 spent 5-20 hours working with teachers,
    other students and family members).
  • In all categories and on both regional and state
    exams, male participants outperformed (sometimes
    significantly) female participants.

13
Participants By Gender
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Compare Gender Performance
17
Looking at the Exam Content
  • Compare performance between concept and problem
    solving abilities.
  • Compare performance between conceptual (rich in
    relationships) and procedural (rules and
    language) knowledge (Hiebert, 1986).
  • Compare performance between the 5 NCTM Content
    Standards.

18
Concepts vs. Problem Solving
  • Concept exams were 2/3 concepts and 1/3
    problem solving.
  • Ex. If a given square has a side 8 inches in
    length and you have to draw a square with four
    times the area of the given square, how many
    inches are in the length of a side of the square
    you have to draw?

19
Concepts vs. Problem Solving
  • Problem solving exams were 3/4 problem solving
    and 1/4 concepts.
  • Ex. Four boys work together painting houses for
    the summer. For each house they get 256. If
    they work four months and their expenses are 152
    per month, how many houses must they paint for
    each of them to have a 1000 at the end of the
    summer?

20
  • Regional exams Students averaged 59 correct on
    problem solving and 42 correct on concepts.
  • State exams This reversed, with 48 correct on
    concepts and 38 correct on problem solving.

21
Conceptual vs. Procedural Knowledge
  • Both regional and state tests had a higher
    percent of conceptual questions (59, 65).
  • Regional exams Students did better on the
    procedural (47 correct) than conceptual
    (39 correct) questions.
  • State exams Performed on both was about 40
    correct, with slight improvement by grade level
    (4th - 35, 5th - 43, and 6 - 53 correct).
  • No significant differences between genders.

22
Mathematical Content in Exams
  • Number/Operation Reg (37), State (28).
  • Ex. Find the number of minutes in the month of
    March.
  • Algebra/Thinking Reg (21), State (28)
  • Ex. Two small pizzas and one large pizza cost
    the same as five small pizzas. If a small pizza
    costs 4, then what does a large pizza cost?

23
  • Geometry Regional (14), State (16)
  • Ex. The mid-points of a square are joined as
    shown. A fraction of the original square is
    shaded. What fractional part of the original
    square is shaded?

24
  • Measurement Regional (20), State (23)
  • Ex. Cheryl is mowing the football field. It is
    100 yards long and 75 feet wide. What is the
    area of this football field in square feet?
  • Data/Probability Reg (8), State (6)
  • Ex. The average monthly rainfall for 6 months
    was 28.5 inches. If it had rained 1 inch more
    each month, what would the average have been?

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Hardest Problems on Regional Exams
  • 2/3 of them were concepts, not problem solving.
  • Example How could you rewrite 12 x 5 12 x 8,
    using the distributive property?
  • 71 measured conceptual knowledge.
  • Example If x is an odd number, how would you
    represent the odd number following it?
  • Number/operation and measurement were again the
    content of the hardest questions.
  • Example If the area of a 1 x 3 rectangle is
    increased by a factor of 16, what are all of the
    possible whole-number dimensions of the new
    rectangle?

29
Gender Issues Concerning Content
  • 6th grade females had more success with number
    and operation (93.8) on the regional concepts
    test than males (59.2). For all other tests and
    content areas, females scored slightly lower than
    males.

30
Procedural Problem Solving (Females Shine) vs.
Creative Problem Solving (Males Shine)
  • A square piece of paper is folded in half along
    the diagonal. The area of the resulting triangle
    is 50 cm2. What was the perimeter of the
    original square?
  • What is the smallest possible sum for all
    Wednesday dates in a 30-day month?

31
Questions Where Females Outperformed Males
  • The following diagram represents what division
    fact?
  • Your teacher tells you to turn to the facing
    pages which sum to 405. To which pages do you
    turn?
  • A 15 minute tape in an answering machine can
    record how many 18 second messages?

32
Questions Where Females Outperformed Males
  • Mad King Ludwig had a castle with a moat around
    it. One could enter the castle yard over 3
    different drawbridges. From the castle yard, one
    could enter the castle through 4 different gates.
    There were 5 different doors through which one
    could enter the throne room. How many different
    ways from outside the castle could one enter the
    throne room?
  • Tyrel gave Tonisha half of his Pokemons. Tonisha
    gave half of these to Erin. Erin kept 8 of them
    and gave the remaining 10 to Seri. How many
    Pokemons did Tyrel give to Tonisha?

33
Questions Where Males Outperformed Females
  • 2/3 of them were problem solving, not concepts.
  • Example What is the smallest positive whole
    number answer possible when you rearrange the
    following seven symbols, using each exactly once?
    ( x - ) 9 2 4
  • There was an even split between conceptual and
    procedural knowledge.
  • 36 of them involved numbers/operations, and
    another 27 of them involved measurement.
  • Example Find the distance between the two
    points (3, 5) and (6, 4).

34
Gender Differences Involving Repeaters
  • For both 5th and 6th grade regional contests, the
    percent of repeating male participants (38, 43)
    was higher than female repeaters (33, 38).
  • 40 of both 5th and 6th grade state qualifiers
    had also qualified for state the previous year
    (45 males, 30 females). 40 of 6th grade state
    qualifiers had also qualified for state 2 years
    previous (43 male, 32 female).

35
Possible Reasons From Literature Review For
Gender Differences
  • The dominance of males in mathematical contests
    can discourage females from pursuing their
    interest in the subject.
  • By the second grade students have already
    identified math and science as male.
  • By third grade, females rated their own
    competence in mathematics lower than that of
    their male classmates, even when they received
    the same or better grades.

36
Possible Reasons From Literature Review For
Gender Differences
  • Young females gain less experience than males
    with core math concepts due to the kinds of toys
    geared toward each gender.
  • From birth, female infants are discouraged from
    risk-taking and from exploring the world around
    them, whereas males are given toys that encourage
    small motor skills and spatial visualization
    skills, both necessary for later development in
    mathematics.
  • The preferred learning style for females is
    working collaboratively rather than
    competitively, and that females would enjoy
    mathematics more and increase their time on task
    if it were taught in a cooperative setting.

37
Possible Reasons From Literature Review For
Gender Differences
  • Self-confidence (or lack thereof) may also be a
    strong contributing factor to why males are
    outperforming females on this contest.
  • The mathematics curriculum at middle school
    emphasizes abstract concepts and spatial
    visualization, two skills that many females have
    not had much experience with in pre-school and
    primary levels.
  • Studies point to parental and societal
    perceptions and teacher behavior and expectations
    as the main reasons that females select out of
    science and mathematics.

38
Sample Questions By Content Standard
Number/Operation
  • Put the following problems in order (listing the
    letter for each) according to the size of their
    answers, smallest first
  • 49.95 X 70
  • 2.49 X 99.9
  • 9.99 X 499
  • 99.9 X 9.80099
  • David has 500 in a savings account. If his
    money earns 6 interest at the end of each year,
    how much money will he have in total after
    collecting his interest for the 6th year?

39
Sample Questions By Content Standard
Algebra/Algebraic Thinking
  • If you multiply a one-digit number by 3, add 8,
    divide by 2, and subtract 6, you will get the
    number you started with back. What is the
    number?
  • 0 gt 2.
  • 1 gt 4.
  • 3 gt 8.
  • 5 gt 12 If the same rule applied to every
    number, then 6 gt ? .
  • What temperature in Fahrenheit is equivalent to
    35 degrees Centigrade?

40
Sample Questions By Content StandardGeometry
  • Thirteen one-inch cubes are put together to form
    the T-figure below. The complete outside of the
    T-figure (including the bottom) is painted red
    and then separated into its individual cubes.
    How many of the cubes have exactly 4 red faces?
  • Find the distance between the points (3,5) and
    (6,4) to the nearest hundredth.

41
Sample Questions By Content StandardMeasurement
  • Cheryl is mowing a ball field. It is 125 yards
    long and 75 feet wide. What is the area of the
    ball field in square feet?
  • When the circumference of a toy balloon is
    increased from 20 inches to 25 inches, the radius
    is increased by?
  • A model car has a scale in which 1/4 inch
    represents 28 inches. If the completed model is
    2 3/4 inches long, how long is the actual car?

42
Sample Questions By Content StandardData and
Probability
  • A motorist drives through three sets of traffic
    lights every day. The probability that the
    motorist has to stop at the first set of lights
    is 0.4, at the second 0.6, and at the third 0.63.
    Each set of lights is independent of the others.
    Calculate the probability that the motorist does
    not have to stop at any of the lights.
  • What number should be added to the following set
    of data so that the mean, median, and mode will
    become the same number?
    91, 93, 93, 95, 95, 98, 100

43
Reference list
  • Ashley, David I. Plymate, Lynda (2004). Gender
    Differences in the Missouri State Elementary Math
    Contest. In the Missouri Journal of Mathematical
    Sciences. Volume 16. Number 1. Winter 2004 pp 40
    50.
  • Plymate, Lynda Ashley, David (2003).
    Elementary Mathematics Contests Student
    Performance on Questions Which Reflect NCTM
    Standards. Teaching Children Mathematics. Vol.
    10 Num. 3 Nov. pp 162-169.
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